When TDA meets geometric group theory: A stratification of barcode space using Coxeter complexes (Adélie Garin, EPFL)

16.04.2024 10:30

At the intersection of data science and algebraic topology, topological data analysis (TDA) is a recent field of study that provides robust mathematical, statistical and algorithmic methods for analysing the topology and geometry underlying complex data. TDA has proven useful in many applications, including biology, materials science and climate science, and continues to evolve rapidly. Barcodes are frequently used invariants in TDA. They provide topological summaries of the persistent homology of a filtered space. Understanding the structure and geometry of the barcode space is therefore crucial for applications. In this talk, we use Coxeter complexes to define new coordinates on the barcode space. These coordinates define a stratification of the barcode space with n bars, where the highest dimensional strata are indexed by the elements of the symmetric group. This creates a bridge between the fields of TDA, geometric group theory and permutation statistics, which could be exploited by researchers in each field.
This presentation is based on joint work with B. Brück. No prerequisites on TDA or Coxeter complexes are required.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Tuesday 16.04.2024, Séminaire "Groupes et géométrie"

entrée libre